Answer:
*look at the step by step*
Step-by-step explanation:
If you plot this on a graphing calculator or Desmos you will see it is always 1-1 (for a given x, one value of y)
The function is zero when x = 7, so touches the x axis at (7,0). To the left of (7,0) funcon is decreasing (as x increases, y decreases), to the right of (7,0) the function is increasing.
so the domain (x values) where f is increasing is x >7 or (7, +∞)
Range of f (possible y values) is [0,+∞)
for the inverse
f (x) = (x-7)2
lets put f(x) = y
y = (x-7) 2
to find the inverse function
get x in terms of y
switch the x and y
y = (x-7)2
√y = x - 7
7 + √y = x
switch x, y
7 + √x = y
y = f-1 (x)
f-1 (x) = 7 + √x
Domain of the inverse : f-1 (x) will exist as long as x >= 0, (so the square root exists) so the domain should be [0, + ∞). However the question states the inverse is restricted to the domain above, so domain is x > 7 or (7, +∞).
Range of the inverse. Obviously is is strictly increasing (as x increases , y increases) so the minimum values must be 7 + √7, and maximum + ∞. So range is ( 7 + √7, + ∞)